I don't think so. The log base 2 is not a built-in function. As far as I know, you would have to use the equivalent log( x ) / log( 2 ) expression.
It is possible to define custom functions that can appear in the formula editor. I do not think that they appear in the New Column Formula menu, though. There are a lot of Community members who are smarter than me, so someone else might have a better answer for you.